Tight projections of frames on infinite dimensional Hilbert spaces

DOI10.7153/OAM-08-58zbMATH Open1433.46010arXiv1211.3360OpenAlexW2963633197MaRDI QIDQ5178315

John Jasper

Publication date: 16 March 2015

Published in: Operators and Matrices (Search for Journal in Brave)

Abstract: We characterize the frames on an infinite dimensional separable Hilbert space that can be projected to a tight frame for an infinite dimensional subspace. A result of Casazza and Leon states that an arbitrary frame for a 2N- or (2N-1)-dimensional Hilbert space can be projected to a tight frame for an N-dimensional subspace. Surprisingly, we demonstrate a large class of frames for infinite dimensional Hilbert spaces which cannot be projected to a tight frame for any infinite dimensional subspace.

Full work available at URL: https://arxiv.org/abs/1211.3360

zbMATH Keywords

framescompressionsprojections of frames

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

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